Recursive economics

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Recursive economics studies decisions that play out over multiple time periods. Unlike the standard neoclassical view, which usually models one-period choices (like a consumer maximizing utility in a single period or a firm maximizing profits in one period), recursive economics looks at how today’s choices affect the future.

In recursive models, agents trade off current benefits and costs with those expected in the future. The key idea is to maximize value or welfare, which is today’s payoff plus a discounted value of future opportunities. Mathematically, this leads to equations like the Bellman equation, which links present rewards to the future value. The approach is often solved using dynamic programming, and it can be described with two-period decisions that build up a longer time path.

The recursive framework has its roots in control theory and the development of dynamic programming by Richard Bellman in the 1950s. Since then, researchers such as Dreyfus, Blackwell, and Howard contributed to the method, and it has been applied widely in economics. One famous early example is Robert Merton’s 1973 work on the intertemporal capital asset pricing model, which uses a recursive, multi-period approach to investors choosing between current income and future income or capital gains.

Today, recursive methods are used in many areas of economics, including macroeconomics, monetary and fiscal policy, economic growth, asset pricing, and firm valuation. They offer powerful tools for solving problems where choices today affect outcomes tomorrow. However, solving high-dimensional recursive models can be computationally challenging, a challenge that researchers continue to address with specialized techniques and textbooks that lay out the theory and applications.